Unstable Entropy and Unstable Pressure for Random Diffeomorphisms with Domination

Xinsheng Wang, Weisheng Wu, Yujun Zhu

Published 2018-11-30Version 1

Let $\mathcal{F}$ be a $C^2$ random dynamical system with $u$-domination. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of $\mathcal{F}$ on the unstable foliation are introduced and investigated. A version of Shannon-McMillan-Brieman Theorem for unstable metric entropy is given, and a variational principle for unstable pressure (and hence for unstable entropy) is obtained. Moreover, as an application of the variational principle, equilibrium states for the unstable pressure are investigated.